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ECON 3410/4410 LECTURE 7 Aggregate demand

dynamics

- Ragnar Nymoen
- 4 October 2007

Overview

- Review of aggregate demand and its components.
- Closed economy, open economy in a later lecture
- Determinants of aggregate investments (ch 15) and

consumption (ch 16), important and volatile

components of aggregate demand - Aggregate demand put together,
- and how monetary policy affects aggregate demand

(ch 17)---the transmission mechanism. - Term structure of interest rates
- Regime dependency of AD curve
- Aggregate demand and aggregate supply
- Short and long-run versions of the closed economy

AS-AD model

Ch 15Private investment

Overview of Q-theory of investment

- The market value of a firm is determined by

discounting future dividends to the owners - By investing in capital, the firm grows and hence

its capacity to generate dividends increases - The cost of investing one unit of capital is

exogenous - This provides an incentive for firms with a high

market value per unit of capital to invest - Definition q the ratio between the market

value of the firm (V) and the replacement value

of its capital stock (K) - Note Q-theory applied to housing investment

(section 15.4) is cursory (you may drop it)

Pricing by arbitrage condition

- Arbitrage condition In every period, stocks and

bonds must yield the same risk-adjusted rate of

return - Vt real stock market value of the firm at the

start of period t - Vet1 expected real stock market value of the

firm at the start - of period t1
- De real expected dividend at the end of the

period t - r real interest rate on bonds
- ? risk premium on shares
- In this way, markets for financial captial and

real captial becomes integrated.

The fundamental value of a firm

- Successive substitution of Vetj gives
- Assume that the future value of the firm Vet1

cannot rise faster than r ? (else it would be

of infinite value), i.e.

The fundamental value of a firm

- Then the infinite sum can be written as
- What does this expression remind you of?
- Interpretation The fundamental value of the firm

equals the present value of expected future

dividends - The role of the interest rate We only assume

that the expected return on shares is

systematically related to the return on bonds - What about investments? The firm must decide

whether to pay out its profits now (as dividends)

or invest it in order to increase profits

(dividends) later Maximize Vt with respect to It

The decision to invest

- Definition qt Vt / Kt the ratio between the

market value of the firm and the replacement

value of its capital stock - Expected value of the firm tomorrow
- ? where we have used

and - Cash flow constraint
- ?e expected profit
- c installation costs
- Assume the following installation cost function

Optimal level of investment depends on q

- Maximization of Vt taking qt as given gives the

following first-order conditions

An example of the investment function

- Assume that in order to simplify the

value of the firm to - Assume furthermore that and
- ? expected dividend pay-out ratio
- ? constant profit share
- Using the definition of q this gives the

investment function

The general investment function

- Abstracting from the functional form the general

investment function is - E index of business confidence
- Note that the risk premium is omitted
- Note that in ch. 17 the level of capital K is

assumed constant and the notation changes

slightly (? is the index of business confidence)

Static investment function

- Note that the rationale for assuming K constant

(despite KtKt-1 It) is that K is a stock

variable, while I is a flow variable. - Hence Kt is close to Kt-1 if the time period is

short, even for large It - However, as we shall see, It may still react

dynamically because of dynamics elsewhere in

the full model.

Ch 16Private consumption

Overview of intertemporal consumption theory

- Diminishing marginal utility of consumption

provides an incentive for consumption smoothing

over time. - Through the capital market, consumers can save or

borrow and thus separate consumption from current

income. - The discounted value of disposable lifetime

income (human wealth) plus the initial stock of

financial wealth represents the consumers

lifetime budget constraint. - In optimum the consumer is indifferent between

consuming an extra unit today and saving that

extra unit in order to consume it tomorrow. - Current consumption will be proportional with

wealth not income. - Note Issues on debt-financed tax cuts and

Ricardian equivalence will be treated later on in

the course.

Intertemporal consumer preferences

- Representative consumer with a two-period utility

function - Properties of the utility function
- the marginal utility of consumption in each

period is positive, but diminishing (provides an

incentive for consumption smoothing) - the consumer is impatient the rate of time

preference ? is positive

Intertemporal budget constraint

- Period 1 budget constraint
- Period 2 budget constraint
- The consumers intertemporal budget constraint
- V financial wealth
- r real rate of interest
- YL labour income
- T net tax payment (taxes minus transfers)
- C consumption

Human wealth and financial wealth

- V1 represents the consumers initial financial

wealth - The present value of disposable lifetime income

can be thought of as human wealth (or human

capital) H - This simplifies the notation of the intertemporal

budget constraint

Optimal intertemporal consumption

- Utility over the consumers life-time becomes (as

a function of C1) - Maximization of U with respect to C1 gives the

following first-order conditions - The Keynes-Ramsey rule

Optimal intertemporal consumption

- In optimum, the marginal rate of substitution

between present and future consumption (MRS) must

equal the relative price of present consumption

(1r)

Example of the consumption function with CES

utility

- The constant (intertemporal) elasticity of

substitution utility function - u(Ct) Ct-1/?
- Insert this into the Keynes-Ramsey rule

Example of the consumption function with CES

utility

- Insert the expression for the optimal C2 in terms

of C1 into the intertemporal budget constraint. - Current consumption C1 is proportional to total

current wealth (not current income). - The propensity to consume wealth is positive, but

less than one.

The general consumption function

- g growth rate of income (increases human

wealth) - Some consumers may be credit constrained, hence

Y1d - In chpt. 17 notation is slightly changed
- The value of financial wealth is treated

implicitly in r - ? is an index of consumer confidence (proxy for

expected income growth)

Relationship to consumtion function in IDM

- In IDM we had a consumption function with fewer

explanatory variables, essentially only

arguments, only Y-T. - We could have added r, for example, but left it

out for simplicity. - On the other hand we introduced lagged C of

course - The IDM specification thus assumes that

adjustment of C to changes in Y-T for example is

all done within the period of analysis.

Ch 17Aggregate demand

Overview over aggregate demand theory with

endogenous monetary policy

- Private investments and consumption are sensitive

to changes in the real interest rate, hence there

is a potential for stabilization policy - The government cares about stabilizing both

output and inflation - In order to achieve the governments objectives,

the central bank sets the nominal short-term

interest rate according to a Taylor rule - The resulting aggregate demand curve will be

downwards-sloping in (y?) space - Important properties of the aggregate demand

curve (the exact slope as well as the shift

properties) will depend on the policy priorities

(implied by the choice of coefficients in the

Taylor rule) - Note We will return to questions about fiscal

policy (public consumption and taxes) later in

the course

Equilibrium condition in the goods market gives

the aggregate demand function Y

- Investments plus consumption aggregate private

demand D - Equlibrium condition for the goods market (closed

economy) - Properties of the aggregate private demand

function

Evidence from Denmark seem to confirm a close

relationship between private sector demand and

the real interest rate over time

The real interest rate and the private sector

savings surplus in Denmark, 1971-2000. Per cent

Source Erik Haller Pedersen, Udvikling i og

måling af realrenten, Danmarks Nationalbank,

Kvartalsoversigt, 3. kvartal, 2001, Figure 6

The long-run aggregate demand function in

log-linearized form

- Assume that for that all arguments in the demand

function are at their long-run (steady state)

values, then long-run aggregate demand function

is - The IAM textbook shows how the aggregate demand

function Y can be log-linearized around its

long-run equilibrium values to give

The real and the nominal interest rate

- The definition of the expected real interest rate
- As long as i and ? are close to zero, we can

approximate the real interest rate - As a first approach we will assume static

expectations

The Taylor-rule as a proxy for monetary policy

- History shows that governments care about

stabilizing both output and inflation. - As a proxy for these policy motives, we can use

the following interest rate rule proposed by John

Taylor - With this rule, y, ? and r will be on their

long-run equilibrium values on average. - ? is interpreted as the inflation target (can be

implicit or explicit). - For the stability of this economy, the parameter

must be h positive so that an increase in

inflation triggers an increase in the real

interest rate (the Taylor principle).

Evidence from the euro area seems to confirm the

Taylor rule as a proxy for monetary policy

The 3 month nominal interest rate and an

estimated Taylor rate for the euro area,

1999-2003. Per cent

Source Centre for European Policy Studies,

Adjusting to Leaner Times, 5th Annual Report of

the CEPS Macroeconomic Policy Group, Brussels,

July 2003

Policy priorities implied by the Taylor rule

coefficients seem to vary across countries

Estimated interest rate reaction functions of

four central banks

1. Source Richard Clarida, Jordi Gali and Mark

Gertler, Monetary Policy Rules in Practice

Some International Evidence, European Economic

Review, 42, 1998, pp. 10331067. 2. Source

Centre for European Policy Studies, Adjusting to

Leaner Times, 5th Annual Report of the CEPS

Macroeconomic Policy Group, Brussels, July 2003.

Aggregate demand curve with endogenous monetary

policy

- The log-linearized version of the aggregate

demand function Y and the Taylor rule can be

combined to an aggregate demand curve in (y?)

space

The shape of the aggregate demand curve will

depend on the priorities of monetary policy

Illustration of the aggregate demand curve under

alternative monetary policy regimes (indicated by

the choice of coefficients h and b in the Taylor

rule)

The transmission mechanism Term structure of

interest rates

- Remember that the rate of interest r in the

demand function is interpretaable as an yield on

long term bonds (10 years for example), a so

called long interest rates - What monetary policy controls (directly or

indirectly) is the very short interest rate, the

money-market interest rate. - How can the central bank control the interest

rate which is relevant for aggregate demand? - Answer No worry! When capital markets are

operating according to theory a change in the

money market rate will be transmitted

automatically to the long rates! - Arbitrage is (again) the mechanism

The expectations theory of the term structure of

interest rates

- Investment decisions depend on the expected cost

of capital over the entire life of the asset

(easily 10 years) - To what extend does the short-term policy rate

influence long-term interest rates? - If short-term and long-term bonds are perfect

substitutes (risk neutral investors) then the

following arbitrage condition will hold - Taking logs and using the approximation ln(1i) ?

I - Alternative Static interest rate expectations

In 2001, U.S. long-term interest rates kept a

steady level as the short-term policy rate fell

The Federal funds target rate (U.S. policy rate)

and the yield on 10 year U.S. government bonds,

2001-2002. Per cent

Source Danmarks Nationalbank

Whatever happened to the money market?

- The Taylor-rule pushes the money market that we

know from the IS-LM model into the background. - This is OK in many ways, as long as it does not

lead to misunderstanding like - There is no role for money in the model
- The money market is always, there it is only that

it is not always specified explixtely.

The money market in a period-to-period equilibirum

Real Money supply

i

Real money demand L(Yt,it)

Mt/Pt

Consider a money targeting regime In each period

the money supply is set by the central bank.

Real Money supply in period t

i

Interest rate in peride t

Real money demand L(Yt,it)

Mt/Pt

Interest rate function in a money targeting regime

The money graph in previous slide defines

it i(Yt, Mt/Pt) where Y and

M/P are regarded as determined outside the money

market, M/P being the policy instrument.

- If we define a long-run interest rate by

inserting the long run values of the arguments in

the i-function and then take the deviation

between it and the long-run rate, we obtain a

function that is qualitatively similar to the

Taylor-rule. With one important difference - In the money targeting regime the derivatives of

the i-function are already given by the

properties of the money demand function. - In the Taylor-rule the corresponding parameters h

and b transpires to be free parameters, to the

chosen by the central bank (see next lecture) - Note IAM p 504-506 contains a more detailed

comparison/derivation of the two interest rate

functions

The money market with a policy determined

interest rate

If the coefficients of the Taylor-rule are

free-parameters, the money market operates like

this

i

Interest rate in period t

M/P

Real money supply In period t

Real money supply is then an endogenous variable.

Since the price level is pre-determined in any

given period, it is the nominal money stock that

adjusts immediately to bring the market into

equilibrium. The Central Bank does this by

market operations.

The AD-schedule is regime dependent

- Although it is OK for some purposes to use the

Taylor-rule as a catch all for monetary policy,

as IAM does, it is also obscuring the important

fact that - The response of aggregate demand (the impact

multipliers of you like) to for example an

increase in g is dependent on the monetary policy

regime. - This point is going to be even more important

when we later move to the open economy.

Aggregate demand dynamics---where is it?

- This lecture was titled aggregate demand dynamics

- But the main impression is that we have

simplified so much that dynamics have almost been

removed from the demand side. - Still there is one source of dynamics left the

real interest rate is and expectations

variable---which is a source of dynamics. - In the next lecture we will utilize this to

establish a long-run and a short-run version of

the AD-AS model. - We will also consider a different model

altogether the real-business cycle model, where

dynamics stems form other sources than

expectations.